Rule utilitarianism is a form of utilitarianism which states that moral actions/right and wrong are those which agree with the rules which lead to the greatest good for the greatest amount of people.

For rule utilitarians, the correctness of a rule is determined by the amount of good it brings about when followed – creating a general rule to live by.

Act utilitarians judge actions in terms of the goodness of their consequences without reference to rules of action – looking at specific scenerios.
An example of Rule Utilitarianism - stresses the greater utility/usefulness of following a general rule, arguing that the practice of following some rule in all instances (always stopping at red lights, for example) will have better consequences overall than allowing exceptions to be made in individual instances, even if better consequences can be demonstrated in those instances.
Why would you ever go through a red light? For an ambulance/pregnancy/the Prime Minister being shot?
Other things being equal people are happier if their society follows rules so people know what types of behaviour they can expect from others in given situations. Therefore utilitarians can justify a system that goes, "Keep to the rules unless there is a strong reason for breaking them."? Rule Utilitarianism is often split between weak and hard ! Can you tell the difference?
A specific criticism of rule utilitarianism states that it collapses into act utilitarianism. David Lyons argued that collapse occurs because for any given rule, in the case where breaking the rule produces more utility, the rule can be sophisticated by the addition of a sub-rule that handles cases like the exception. This process holds for all cases of exceptions, and so the ‘rules’ will have as many ‘sub-rules’ as there are exceptional cases, which, in the end, makes an agent seek out whatever outcome produces the maximum utility – and so becomes such a specific rule that it only works for that given scenario…